13 Choose 3

Combination Calculator
Total items (n)
Items chosen (k)

What is 13 choose 3?

Answer

13 choose 3 is
286

Order doesn't matter, no repeats: 286 ways to choose 3 of 13 items.

C(13, 3) = 13! / (3! · 10!)

= (13 × 12 × 11) / (3 × 2 × 1)
= 1,716 / 6

= 286

If order matters (permutations): P(13, 3) = 13 × 12 × 11 = 1,716 — each combination in 3! = 6 orders.

Row 13 of Pascal's triangle
k13 choose k
01
113
278
3286
4715
51,287
61,716
71,716
81,287
9715
10286
1178
1213
131

Row sum: 213 = 8,192 — all subsets of 13 items.

See Also

Recalculate with different values ↑

n choose 3 for other n

n choose 3Answer
6 choose 320
7 choose 335
8 choose 356
9 choose 384
10 choose 3120
11 choose 3165
12 choose 3220
13 choose 3286
14 choose 3364
15 choose 3455
16 choose 3560
17 choose 3680
18 choose 3816
19 choose 3969
20 choose 31,140

FAQ

What is 13 choose 3?

13 choose 3 is 286

Why is 13 choose 3 the same as 13 choose 10?

Every way to choose 3 of 13 items leaves exactly 10 behind, so choosing 3 and choosing which 10 to leave out are the same count: 13 choose 3 = 13 choose 10 = 286. In the formula n! / (k! (n − k)!) the two factorials below just swap places.

How many ways are there if order matters?

P(13, 3) = 1,716. Each of the 286 combinations can be put in order in 3! = 6 ways, so permutations = combinations × k!: P(n, k) = n! / (n − k)!.

See Also